6. Consider the following problem: max z = 2x1 + x2 s.t. x2 < 10 2x1 + 5x2 < 60 X1 + x2 < 18 3x1 + x2 < 44 X1, x2 > 0. Construct the dual problem. Use the fact that x1 = 13 and x2 = to identify the nonbasic variables and basic variables for the optimal solution to the dua complementary slackness. 5 is optimal for the

Q: 1. Obtain the initial basic feasible solution to the following transportation problem using north…

A: We have the initial table as, We have Total supply = 14 + 16 + 5 = 35 and Total demand = 6 + 10 +…

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Q: 4. Given the LP model Maximize Z =10 x1 +15x2 +20x3 Subject to 2 x1+4 x2+6 x3524 3 x1+9 x2+6 x3530…

A: To Determine :-  a. The range of objective function coefficient c2 of variable x2 such that the…

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A: Below are the screenshots attached of Excel Solver Solution

Q: Here is the original LP max z = 3x1 + 2x2 < 100 < 80 < 40 s.t. 2x1 + ¤2 2i + x2 and the optimal…

A: Ans1: There is no allowable increase to constraint 2. This is because the value is 80. Ans 2:There…

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Q: 4. The ICARE Company has three plants located throughout a state with production capacity 50, 75 and…

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A: We  have  max Z=-x1+2x2                   s.t.                   x1+x2≤6                   -x1+2x2≤8…

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Q: QUESTION 14 Calculate the maximum value of 9x + 6y subject to the constraints below: 2x + 2y s 18 x…

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A: The simplex method (BigM method) Max z=y1+y2-2y3subject to y1+2y2≤5y1-y2-3y3≤4and y1≥0,y2≥0,y3≥0 The…

Q: sider the transportation problem presented in the following table:   D1 D2 D3 D4 SUPPLY S1 19 30 50…

A: Given: consider the transportation problem presented in the following table:   D1 D2 D3 D4 SUPPLY…

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A: Please see the attachment

Q: Consider the following linear program : z = 6x1 + 6x2 + 10x3 → min s.t. 4x1 + 3x2 + 2x3 ≥ 16 x1 +…

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Q: Destination 2 3 4 Supply 1 50 2 2 2 30 3 5 30 Demand 30 35 20 25 Source

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Q: 1. Consider the problem below: Min (z) = -2x-×2 Subject to: X1 + X25 5 2x1 + 3x2 S 12 X1 5 4 X1, X2…

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Q: Solve for the optimal investment and capital profiles for the following problem by applying optimal…

A: We will use Euler-Lagrange equation to find the optimal solution.

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Q: 4. Consider the feasible region below. 12 (4, 10) 10 (0, 8) 80 (8, 6) 6 4 |(10, 2) (0, 2) 2 6 8 10…

A: 4. Observe the feasible region.

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A: The solution is given below

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Q: Consider the following LP: Minimize z = 4x, + x2 subject to 3x, + x = 30 4x, + 3x, 2 60 X + 2x2 s 40…

A: Introduce slack, surplus, artificial variables: Min z=4x1+x2+0S1+0S2+MA1+MA2 subject to…

Q: 18. f (z,y) = e²³y²–2zy²+y?

A: The function is given as, fx,y=ex2y2-2xy2+y2 Differentiate w.r.t. x,…

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A: If the primal problem is of the form Minimize z=CY Subject to AY&gt;=b Y&gt;=0 Then it's dual…

Q: corresponding graph below. Maximize z = 5x + 4y Subject to: 3x + 2y = 8 x >= 0 y >= 0   From the…

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Q: Suppose a unit of capital costs $2 and a unit of labour costs $4. The production function is Q = 6KL…

A: Production Function is Q = 18 KL + 6L2   .......(1) (a)  We have to maximize (1) subject to 2K + 4L…

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Q: 3. As follows: 6 Consider the following LP and its optimal tableau (Table 55): max z 3x1 + x2 X3…

A: Consider the LP  max z=3x1 + x2 -x3  such that  2x1 + x2 + x3 ≤ 8  4x1 x2 -x3 ≤ 10 x1,x2,x3 ≥ 0

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Q: 1. For this and the following three problems, consider a partial equilibrium two households with…

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A: For convenience, we take x=x1, y=x2, x=x3 and P=Z.

Q: 2. Obtain the initial basic feasible solution to the following transportation problem using north-…

A: Given table with Demand and supply is as follows Given transportation problem is balanced so apply…

Q: 2. Obtain the initial basic feasible solution to the following transportation problem using north-…

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Q: 4. Regarding the labor-leisure trade off. Assume Sue Ellen Walton has the utility function U(C,L) =…

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Q: Consider the following LPP: Min Z 3 3X, + Х+ Xз Such that: X — 2X + Xз <11, -4X; + X, + 2X3 2 3…

A: Optimal primal table is given in the problem We know that optimal solution of both the primal and…